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The present invention relates generally to apparatus and methods of measuring the shape and thickness of wafers, and more specifically to wafer shape and thickness measuring apparatus and methods that employ symmetric and asymmetric instrument error signatures.
Semiconductor circuits are grown on semiconductor wafers that are being manufactured in increasingly larger diameters. The fineness of the circuit lines making up the semiconductor circuits requires a precise focus on an extremely flat wafer. Test equipment has been developed to measure the shape and thickness of wafers, but the quality of the measurement is limited by the error that is induced by the equipment. In test equipment that grips the wafers by the edge and measures the wafer without touching either surface, the measurement precision and consistency have been good when wafers are placed on the test equipment at the same angular orientation. The shape accuracy has not been as good when the wafers are measured at various angular orientations. The measurements from this equipment may be degraded by two types of errors; symmetrical error that is independent of the orientation of the wafer to the grippers and asymmetric error which is correlated with the angular orientation of the wafer on the instrument.
Wafer shape can to be determined with a relatively low spatial frequency resolution. When a wafer is measured while the load angle between measurements is varied, a strong signature that also rotates with the load angle is observed. This instrument signature is independent of the wafer shape and is fairly stationary. A technique that strongly rejects wafer shape can be used to obtain most of this signature, which is called the symmetric signature. The remainder that is not removed by this first step is called the asymmetric signature. The asymmetric instrument signature is evaluated statistically by considering the residual errors in the data. The total corrector is defined by adding both the symmetric and the asymmetric instrument signature. Other aspects, features, and advantages of the present invention are disclosed in the detailed description that follows.